theorem Th15:
  for f be FinSequence of REAL holds
    k in dom (f/^n) & n in dom f implies n+k in dom f
  proof
    let f be FinSequence of REAL;
    assume
    A1: k in dom (f/^n) & n in dom f; then
    len (f|n) + k in dom ((f|n)^(f/^n)) by FINSEQ_1:28; then
    n+k in dom ((f|n)^(f/^n)) by A1,Th10;
    hence thesis by RFINSEQ:8;
  end;
